双线性强化隧道和桩孔三剪弹塑性解
Elastic-plastic solutions of bilinear strain-hardening tunnel and pile cavity based on tri-shear failure criterion

将隧道和桩孔简化为厚壁圆筒,基于三剪强度准则和双线性强化模型,考虑材料的应变强化和中间主应力效应,推导了厚壁圆筒在均匀内外压作用下的弹塑性极限解,并给出恒定外压条件下塑性区半径与内压的关系式,分析了强化模量系数、半径比、中间主应力与材料强度拉压异性对厚壁圆筒弹塑性极限解的影响规律。研究结果表明:所得弹塑性极限解克服了Tresca屈服准则与Mises屈服准则未考虑拉压异性,Tresca屈服准则与Mohr-Coulomb屈服准则未考虑中间主应力与双剪强度理论极限解存在滑移面突变现象的不足; 弹塑性极限解均随半径比与中间主应力影响系数的增大而增大,随拉压强度比的增大而减小,外压对极限内压的影响程度随着拉压强度比的增大而减小; 当强化模量系数为0.1、半径比为2时,考虑强化效应的塑性极限内压比不考虑时相对增大10%以上,随着半径比增大到4,塑性极限内压比不考虑强化效应时相对增大38%以上,强化效应影响更加明显,故对于存在应变强化效应的材料,采用双线性强化模型的分析结果更接近工程实际; 当不考虑中间主应力与应变强化时,土体的极限扩孔压力弹塑性极限解与Vesic解相差在0.02%以内,当考虑了土体的中间主应力和应变强化效应后,塑性区半径与内半径比为10时,弹塑性极限解分别是Vesic解的1.06、1.81倍,因此,基于Vesic解的极限扩孔压力过于保守。
Tunnel and pile cavity were simplified as thick-walled cylinders, the effects of strain hardening and intermediate principal stress were considered, the elastic-plastic limit solution of thick-walled cylinder under uniform internal and external pressures was deduced based on the tri-shear failure criterion and the bilinear strain-hardening model, the relationship of internal pressure and elastic-plastic radius under constant external pressure was given, and the effects of many parameters on the limit solution of thick-walled cylinder were discussed, including strengthening modulus, radius ratio, intermediate principal stress and material strength heterogeneity of tension and compression. Research result shows that the proposed solution can overcome the deficiencies of material strength heterogeneity of tension and compression ignored by Tresca and Mises yield criteria, the intermediate principal stress ignored by Tresca and Mohr-Coulomb yield criteria, as well as the abrupt changing phenomenon of slip plane in twin shear strength theory. The limit solution increases with the radius ratio and the intermediate principal stress coefficient, but decreases with the tension-compression strength ratio. The effect of external pressure on the limit internal pressure decreases with the tension-compression strength ratio. Compared with no considering strengthening modulus, when the strengthening modulus is 0.1 and the radius ratio is 2, the plastic limit internal pressure increases by more than 10%. When the radius ratio increases to 4, the plastic limit internal pressure increases by more than 38%, so the strengthening effect is more obvious. Obviously, for the material with strain hardening effect, the result analyzed by the bilinear strain-hardening model is closer to the engineering practices. When the intermediate principal stress and the strain hardening are not considered, the differences of limit expansion soil pressures calculated by the proposed solution are within 0.02%